Dag representation of basic blocks

Dag representation of basic blocks

• 1.
  V.JOTHI LAKSHMI
• 2.
   Useful datastructures for implementing transformations on basic blocks  Gives a picture of how value computed by a statement is used in subsequent statements  Constructing DAG from 3 address statements is good way of determining common sub-expressions  A dag for a basic block has following labels on the nodes  Leaves are labeled by unique identifiers, either variable names or constants  Interior nodes are labeled by an operator symbol  Nodes are also optionally given a sequence of identifiers for labels 2
• 4.
  1. t1 :=4 * i 2. t2 := a[t1] 3. t3 := 4 * i 4. t4 := b[t3] 5. t5 := t2 * t4 6. t6 := prod + t5 7. prod := t6 8. t7 := i + 1 9. i := t7 10. if i <= 20 goto (1) 4 + prod0 * [ ] [ ] * i04 ba + 1 20 <= t1 t4 t5 t6 t7 (1) t3 t2 prod i
• 5.
   Construct adag for a basic block.  Process each statement of the block inturn.  Statement of the form x:=y+z  Look for the nodes that represent the “current” values of y and z.  These could be leaves/interior nodes of dag  If y & z has been evaluated by previous statements of block.  We create a node labeled + and give it two children  Left –node for y right- node for z 5
• 6.
   Input -basic block.  Output - label for each node. label is an identifier for leaves. label is an operator symbols for interior nodes. each node has list of identifiers.  Method - create nodes with one or two children left & right. create linked list of attached identifiers for each node. maintain all identifiers for which a node is associated. node (identifier) represents value that identifier has the current point in dag construction process. Symbol table record for identifier- indicate the value of node(identifier). 6
• 7.
  Given a functionnode(identifier) – it returns the node currently associated with the identifier. Statement types(i) x := y op z (ii)x := op y (iii) x := y 1. If node(y) is undefined then create a leaf labeled y and this is now node(y) in case of x = y op z; do the same for z. 2.Determine if there is a node labeled “op” with node(y) & node(z) as the left and right children in case of x = y op z. 3.Determine whether there is a node labeled op ,whose lone child is node(y) , let n be node(y). 7
• 8.
  S1 = 4* i S2 = addr(A)-4 S3 = S2[S1] S4 = 4 * i S5 = addr(B)-4 S6 = S5[S4] S7 = S3 * S6 S8 = prod+S7 prod = S8 S9 = I+1 I = S9 If I <= 20 goto (1) 8 S1 = 4 * i S2 = addr(A)-4 S3 = S2[S1] S5 = addr(B)-4 S6 = S5[S4] S7 = S3 * S6 prod = prod + S7 I = I + 1 If I <= 20 goto (1)
• 9.
   Consider following basic block t1= a + b t2 = c + d t3 = e –t2 X = t1 –t3 and its DAG 9 - + a b - e + c d X t3 t2 t1
• 10.
  DAGs are usefulfor:  Removing common local sub-expressions.  Renaming temporaries.  Finding names used inside the block but evaluated outside.  Finding statements in the block that could have their computed values used outside the block.  Statements that can be reordered (or executed in parallel). 10
• 11.
  x :=a[i] x:=a[i] a[j] :=y (9.5) z :=x  (9.6) z :=a[i] a[j] :=y  Both compute different values for z in case i=j and y!=a[i].When we assign to an array a, we may be changing the r-value of expression a[i],even though a and i do not change . It is therefore necessary that when processing an assignment to array a , we kill all nodes labeled [],whose left arg is + or – constant.
• 13.
   *p :=w,where p is pointer. If we do not know what p might point to , every node currently in the DAG being built must be killed in the sense above.  If p could only point to r or s , then only node(r) and node(s) must be killed.
• 14.
   A procedurecall in a basic block kills all nodes , since in the absence of knowledge about the called procedure , we must assume that any variable may be changed as a side effect.